# Solve for x, log_10 (x^2 + 1) = 1

Neethu | Certified Educator

Given:

log_{10}(x^2+1)=1

We have to solve for x.

So we can write,

x^2+1=10

i.e. x^2=9

which means \mathbf{x=\pm 3}

tonys538 | Student

The equation log_10(x^2+1) = 1 has to be solved for x.

For three positive numbers a, b and c, if log_a b = c then we can say b = c^a .

Given the equation log_10 (x^2 +1) = 1 , as the base of logarithm is 10:

x^2 + 1 = 10^1

x^2 + 1 = 10

x^2 = 9

x = +-3

The value x can take on both positive as well as negative values as x^2 is positive and so is x^2 + 1.

atyourservice | Student

log_10 (x^2 + 1) = 1

The first step is to set this problem up in the exponential form:

b^y=x

we know that the y will b 1 because log is the exponent and the problem tells us log = 1

10^1 = x^2 + 1

simplify:

10 = x^2 +1

now subtract 1 from both sides to get x^2 alone:

9 = x^2

now we take the square root of both numbers

sqrt(9) = sqrt(x^2)

+- 3 = x

to check:

log_10 (3^2 + 1) =

log_10 (9 + 1) =

log_10 (10) =

log (x) / log(b)

log(10)/ log(10) = 1

same goes for -3 because -3^2 is still 9